instructions Introduce the problem first. You may paraphrase the problem statement. Write in complete sentences! You can center important equations, but they should still be part of your narrative flow. Write as if you were explaining the solution to another Math 121 student who hasn't seen the project yet. Your solution should be organized and have enough detail so that the reader can easily follow it.

1) (5 points) If a spherical weather balloon has radius r feet, then the volume of the balloon is given by V = 4 3 r3 (a) Find the rate of change of the volume of the balloon with respect to the radius of the balloon at the instant when r = 2. Be sure to include units

2)) Suppose that the balloon is punctured and is slowly deflating so that the radius (in feet) of the balloon t hours after the puncture is given by the function r(t). Find an expression for the rate of change of the volume of the balloon with respect to time. What are the units of this rate? How is this rate different from the one in part (a)?

3) ) If the radius is decreasing at a constant rate of 1 ft/hr, build on your work in parts (a) and (b), to find the rate of change of the volume of the balloon with respect to time at the instant when r = 2. Be sure to include units.